Problem 17E
Problem 17E
Let X ~ Geom(p), let n be a non-negative integer, and let Y ~ Bin(n, p). Show that P(X = n) = (l/n)(1/n)p(Y=1).
Step-by-Step Solution:
Solution :
Step 1 of 1:
Given and
Where mean and variance
.
Here non-negative integer is n.
Our goal is :
We need to prove that P(X=n)=.
Now we have to prove that P(X=n)=.
P(X=n)=
The formula of the geometric distribution is
P(X=n)=
Where q = (1-p)
So P(X=n)=
Then,
P(X=n)=
The formula of the binomial distribution is
Here the probability of X is n and the probability of Y is 1.
P(X=n)=
Here and
= p.
P(X=n)=
Therefore P(X=n)=.
Step 2 of 1
